June 2023
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The Drinfeld double associated to the weak multiplier Hopf (-) algebra pairing is constructed. We show that the Drinfeld double is again a weak multiplier Hopf (-) algebra. If A and B are algebraic quantum groupoids, then so does the double. We also prove the correspondence between modules over the Drinfeld double and Yetter-Drinfeld modules. Finally, we prove that the double is a quasitriangular weak multiplier Hopf algebra.